$A, B, C$ and $D$ are square matrices such that $A+B$ is symmetric, $A-B$ is skew-symmetric and $D$ is the transpose of $C$. If $A=\left[\begin{array}{ccc}-1 & 2 & 3 \\\\ 4 & 3 & -2 \\\\ 3 & -4 & 5\end{array}\right]$ and $C=\left[\begin{array}{ccc}0 & 1 & -2 \\\\ 2 & -1 & 0 \\\\ 0 & 2 & 1\end{array}\right]$, then the matrix $B+D=$

If $A$ is square matrix and $A^2+I=2 A$, then $A^9=$

$\operatorname{det}\left[\begin{array}{ccc}\frac{a^2+b^2}{c} & c & c \\\\ a & \frac{b^2+c^2}{a} & a \\\ b & b & \frac{c^2+a^2}{b}\end{array}\right]=$

The system of simultaneous linear equations

$$ \begin{aligned} & x-2 y+3 z=4,3 x+y-2 z=7 \\ & 2 x+3 y+z=6 \text { has } \end{aligned} $$